Theory of Real Functions Tuition Class In Noida
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It is a basic course on the study of real valued functions that would develop
an analytical ability to have a more matured perspective of the key concepts of calculus, namely, limits, continuity, differentiability and their applications. Hence, Join Best Online Math Tutor In Noida.
Course Learning Outcomes: This course will enable the students to learn
i) To have a rigorous understanding of the concept of limit of a function.
ii) The geometrical properties of continuous functions on closed and bounded intervals.
iii) The applications of mean value theorem and Taylor’s theorem.
Limits of functions (approach), Sequential criterion for limits, Divergence criteria, Limit theorems, One-sided limits, Infinite limits and limits at infinity. Hence, Limits of Functions Tuition Class In Noida.
Continuous functions, Sequential criterion for continuity and discontinuity, Algebra of continuous functions, Properties of continuous functions on closed and bounded intervals; Uniform continuity, Non-uniform continuity criteria, Uniform continuity theorem. Hence, Continuous Functions and their Properties Tuition Class In Noida.
Differentiability of a function, Algebra of differentiable functions, Carathéodory’s theorem and chain rule; Relative extrema, Interior extremum theorem, Rolle’s theorem, Mean- value theorem and its applications, Intermediate value property of derivatives – Darboux’s theorem. Hence, Derivability and its Applications Tuition Class In Noida.
Taylor polynomial, Taylor’s theorem with Lagrange form of remainder, Application of Taylor’s theorem in error estimation; Relative extrema, and to establish a criterion for convexity; Taylor’s series expansions of , sin x and cos x. Hence, Taylor’s Theorem and its Applications Tuition Class In Noida.